Finite Group Databasebeta

← #7632336

Subgroups — #7632336

Order 512.

8288 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3516C211yesmaximal, characteristic, complemented
2C22×#520C211yesmaximal, characteristic, complemented
3#36581C213yesmaximal, complemented
4#36578C211yesmaximal, characteristic, complemented
5#36546C213yesmaximal, complemented
6Q8×#123C211yesmaximal, characteristic, complemented
7#36529C213yesmaximal, complemented
8#36528C213yesmaximal, complemented
9#36429C211yesmaximal, characteristic, complemented
10#36428C211yesmaximal, characteristic, complemented
11#35831C212yesmaximal, complemented
12#35816C212yesmaximal, complemented
13#35787C216yesmaximal, complemented
14#35772C216yesmaximal, complemented
15#35625C216yesmaximal, complemented
16#35539C216yesmaximal, complemented
17#35302C213yesmaximal, complemented
18#35236C213yesmaximal, complemented
19#34965C213yesmaximal, complemented
20#34877C213yesmaximal, complemented
21#34313C212yesmaximal, complemented
22#34312C212yesmaximal, complemented
23Q8×#117C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25#3516—216no—
26C2×#557C2211yescharacteristic, complemented
27C2×#556C2213yescomplemented
28C2×#554C2213yes—
29C2×#553C2213yes—
30C2×#552C2213yescomplemented
31C2×#550C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#548C2212yes—
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic, complemented
36C2×#542C2213yescomplemented
37C2×#541C2213yescomplemented
38C2×#529C2213yes—
39C2×#529C2213yes—
40C2×#520—216no—
41C2×#520C2212yes—
42C2×#520C2216yes—
43C2×#520C2216yes—
44C2×#520C2212yes—
45C2×#520C2211yescharacteristic, complemented
46C2×#519C2211yescharacteristic, complemented
47C22×C4×Q8C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic
49C22×C4×D4C2213yes—
50C22×C4×D4C2213yes—
51C22×#117C2213yes—
52C23×C4⋊C4C2213yes—
53#2855C2213yes—
54#2854C2213yes—
55#2848C2213yes—
56#2848C2216yes—
57#2847C2213yes—
58#2847C2216yes—
59#2636C2216yescomplemented
60#2636C2216yescomplemented
61#2629C2216yescomplemented
62#2620C2216yescomplemented
63#2611C2216yescomplemented
64#2610C2216yescomplemented
65#2609C22112yescomplemented
66#2603C22112yescomplemented
67#2601C22112yescomplemented
68#2601C2216yescomplemented
69#2601C2216yescomplemented
70#2591C2213yes—
71#2583C2213yes—
72#2579C2216yes—
73#2566C2216yescomplemented
74#2562C2216yescomplemented
75#2561C2213yes—
76#2544C2216yescomplemented
77#2540C2216yescomplemented
78#2539C2213yes—
79#2538C2216yescomplemented
80#2537C2216yescomplemented
81#2534C2216yes—
82#2504C2213yes—
83#2502C2213yes—
84#2487C2213yes—
85#2487C2213yes—
86#2481C22112yescomplemented
87#2473C22112yescomplemented
88#2467C22112yescomplemented
89#2463C22112yescomplemented
90#2460C22112yescomplemented
91#2456C22112yescomplemented
92#2454C2216yescomplemented
93#2452C2216yescomplemented
94#2449C22112yescomplemented
95#2448C2216yescomplemented
96#2446C2216yescomplemented
97#2443C22112yescomplemented
98#2442C2216yescomplemented
99#2440C2216yescomplemented
100#2435C2213yes—
101#2433C2213yes—
102#2432C2216yes—
103#2431C2216yes—
104#2428C2216yescomplemented
105#2427C2216yescomplemented
106#2423C2216yescomplemented
107#2421C2216yescomplemented
108#2417C2216yescomplemented
109#2416C2216yescomplemented
110#2413C2211yescharacteristic
111#2413C2213yes—
112#2411C2213yes—
113#2411C2213yes—
114#2411C2216yes—
115#2408C2213yes—
116#2408C2213yes—
117#2407C2216yes—
118#2407C2216yes—
119#2396C2216yescomplemented
120#2392C2216yescomplemented
121#2392C22112yescomplemented
122#2367C2216yescomplemented
123#2366C2216yescomplemented
124#2363C2216yescomplemented
125#2361C2216yescomplemented
126#2361C2216yescomplemented
127#2360C2216yescomplemented
128#2355C2216yescomplemented
129#2352C2216yescomplemented
130#2351C2212yescomplemented
131Q8×C4⋊C4C2212yescomplemented
132Q8×C4⋊C4C2212yescomplemented
133D4×C4⋊C4C2216yescomplemented
134#2345C2213yes—
135#2345C2213yes—
136#2341C2212yes—
137#2341C2212yes—
138#2341C2212yescomplemented
139Q8×C22⋊C4C2211yescharacteristic
140Q8×C22⋊C4C2211yescharacteristic
141Q8×C22⋊C4C2212yescomplemented
142#2324C2216yescomplemented
143#2324C2216yescomplemented
144#2324C2216yescomplemented
145#2323C2216yescomplemented
146C4×#127C2216yescomplemented
147C4×#124C2216yescomplemented
148C4×#123C2213yes—
149C4×#123C2213yes—
150C4×#120C2213yes—
151C4×#120C2213yes—
152C4×#120C2216yes—
153C4×#120C2216yes—
154#2295C2216yescomplemented
155#2293C2216yescomplemented
156#2293C2216yescomplemented
157#2285C2213yes—
158C42×Q8C2212yescomplemented
159C4×#117C2213yes—
160C22×#41—216no—
161C22×#41—28no—
162C22×#41C2316yes—
163C22×#41C2311yescharacteristic
164C22×#41C2312yes—
165C23×Q8C2311yescharacteristic
166C23×Q8C2311yescharacteristic
167C23×D4C2313yes—
168C24×C4C2313yes—
169C24×C4C2316yes—
170#557—28no—
171#556—224no—
172#554—224no—
173#553—224no—
174#552—224no—
175#550—216no—
176D4×Q8—28no—
177#548—216no—
178#548—28no—
179#548—28no—
180#542—224no—
181#541—224no—
182C2×C4⋊Q8C2313yes—
183C2×C4⋊Q8C2313yes—
184C2×#127C2316yes—
185#529—224no—
186#529—224no—
187C2×#126C2316yes—
188C2×#126C2313yes—
189C2×#126C2313yes—
190C2×#126C2316yes—
191C2×#125C2313yes—
192C2×#125C2313yes—
193C2×#125C2313yes—
194C2×#125C2316yes—
195C2×#124C2313yes—
196C2×#124C2313yes—
197C2×#124C2316yes—
198C2×#124C2313yes—
199C2×#123C2311yescharacteristic
200C2×#123C2313yes—
201C2×#123C2311yescharacteristic
202C2×#123C2316yes—
203C2×#123C2313yes—
204C2×C22⋊Q8C2313yes—
205C2×C22⋊Q8C2316yes—
206C2×C22⋊Q8C2313yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C2313yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C23112yes—
212C2×#121C2316yes—
213C2×#121C2316yes—
214C2×#121C2316yes—
215C2×#121C2313yes—
216C2×#121C2313yes—
217C2×#121C2313yes—
218C2×#121C23112yes—
219C2×#120C2313yes—
220C2×#120C2313yes—
221C2×#120C2316yes—
222#520—216no—
223#520—248no—
224#520—216no—
225#520—248no—
226#520—28no—
227#519—28no—
228C2×C4×Q8—28no—
229C2×C4×Q8D4116yescomplemented
230C2×C4×Q8C2313yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2316yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2313yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2313yes—
243C2×C4×D4—224no—
244C2×C4×D4—224no—
245C2×C4×D4C2313yes—
246C2×C4×D4C2316yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2313yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C23112yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C23112yes—
261C2×C4×D4C23112yes—
262C2×#117—224no—
263C2×#117C2316yes—
264C2×#117C2313yes—
265C2×#117C2313yes—
266C2×#117C2316yes—
267C2×#117C2316yes—
268C2×#117C2313yes—
269C2×#117C2316yes—
270C2×#117C2316yes—
271C2×#117C2311yescharacteristic
272C2×#117C2313yes—
273C22×C4⋊C4—224no—
274C22×C4⋊C4C2313yes—
275C22×C4⋊C4C2313yes—
276C22×C4⋊C4C2316yes—
277C22×C4⋊C4C2313yes—
278C22×C4⋊C4C2316yes—
279C22×C4⋊C4C23112yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2313yes—
282C22×C22⋊C4C2313yes—
283C22×C22⋊C4C2313yes—
284C22×C42C2313yes—
285C22×C42C2313yes—
286#400C2316yes—
287#400C2316yes—
288#400C2316yes—
289#399C2316yes—
290#399C2316yes—
291#399C2316yes—
292#398C23112yes—
293#398C2316yes—
294#398C2312yes—
295#398C2316yes—
296#398C23112yes—
297#397C2316yes—
298#397C23112yes—
299#396C2316yes—
300#396C23112yes—
301#396C23112yes—
302#396C2312yes—
303#396C2316yes—
304#396C23112yes—
305#396C2316yes—
306#395C2316yes—
307#394C2316yes—
308#394C2316yes—
309#394C2316yes—
310#394C23112yes—
311#394C2316yes—
312#394C2316yes—
313#394C23112yes—
314#394C23112yes—
315#393C2316yes—
316#392C23112yes—
317#392C2316yes—
318#392C2316yes—
319#392C2316yes—
320#391C2316yes—
321#391C2316yes—
322#391C2316yes—
323#391C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C23112yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2316yes—
341#389C2316yes—
342#389C2316yes—
343#389C2316yes—
344#389C2312yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C23112yes—
349#388C23112yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C23112yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2312yes—
358#387C23112yes—
359#387C23112yes—
360#387C23112yes—
361#387C23112yes—
362#387C2316yes—
363#387C2316yes—
364#386C2313yes—
365#386C2316yes—
366#386C23112yes—
367#386C23112yes—
368#386C23112yes—
369#386C2311yescharacteristic
370#386C2313yes—
371#386C2313yes—
372#386C23112yes—
373#386C2316yes—
374#386C2316yes—
375#386C23112yes—
376#386C23112yes—
377#385C23112yes—
378#385C23112yes—
379#385C2313yes—
380#385C23112yes—
381#385C2316yes—
382#385C23112yes—
383#385C23112yes—
384#385C2311yescharacteristic
385#385C2313yes—
386#385C2313yes—
387#385C23112yes—
388#385C2316yes—
389#385C2316yes—
390#384C2316yes—
391#384C2316yes—
392#382C2316yes—
393#382C2316yes—
394#381C2311yescharacteristic
395#381C2313yes—
396#380C23112yes—
397#380C23112yes—
398#380C2316yes—
399#380C2316yes—
400#380C2316yes—
401#380C2316yes—
402#380C2316yes—
403#380C2313yes—
404#380C2313yes—
405#379C2313yes—
406#379C2313yes—
407#379C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2316yes—
411C4×C4⋊C4C2316yes—
412C4×C4⋊C4C2316yes—
413C4×C4⋊C4C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C23112yes—
425C4×C22⋊C4C23112yes—
426#376C2316yes—
427C43C2316yes—
428C25C2413yes—
429C2×#41—2128no—
430C2×#41—224no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—224no—
436C2×#41—224no—
437C2×#41#41116yes—
438C22×Q8—28no—
439C22×Q8—24no—
440C22×Q8—28no—
441C22×Q8C2×D418yes—
442C22×Q8C2413yes—
443C22×Q8C2413yes—
444C22×Q8C2413yes—
445C22×Q8C2411yescharacteristic
446C22×D4—224no—
447C22×D4—212no—
448C22×D4C2416yes—
449C22×D4C2413yes—
450C22×D4C2411yescharacteristic
451C22×D4C2413yes—
452C22×D4C2416yes—
453C22×D4C2416yes—
454C22×D4C2416yes—
455C22×D4C24112yes—
456C22×D4C2413yes—
457C23×C4—212no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4—812no—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2416yes—
464C23×C4C2413yes—
465C23×C4C2413yes—
466C23×C4C2411yescharacteristic
467C23×C4C2413yes—
468C23×C4C2416yes—
469C23×C4C2413yes—
470C23×C4C24112yes—
471C23×C4C24112yes—
472C23×C4C2416yes—
473C23×C4C2413yes—
474C4⋊Q8—212no—
475C4⋊Q8—212no—
476#127—224no—
477#126—224no—
478#126—224no—
479#126—212no—
480#126—212no—
481#125—224no—
482#125—212no—
483#125—212no—
484#125—212no—
485#124—212no—
486#124—224no—
487#124—212no—
488#124—212no—
489#123—24no—
490#123—212no—
491#123—224no—
492#123—24no—
493#123—46no—
494C22⋊Q8—212no—
495C22⋊Q8—212no—
496C22⋊Q8—212no—
497C22⋊Q8—212no—
498C22⋊Q8—224no—
499C22⋊Q8—212no—
500C22⋊Q8—224no—
501C22⋊Q8—812no—
502#121—224no—
503#121—224no—
504#121—212no—
505#121—212no—
506#121—224no—
507#121—212no—
508#121—812no—
509#120—212no—
510#120—412no—
511#120—46no—
512C4×Q8—224no—
513C4×Q8—28no—
514C4×Q8—24no—
515C4×Q8—24no—
516C4×Q8—28no—
517C4×Q8—28no—
518C4×Q8—212no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8C2×D418yes—
522C4×Q8C2×D4124yes—
523C4×Q8C2×D418yes—
524C4×Q8C2×D4124yes—
525C4×D4—212no—
526C4×D4—212no—
527C4×D4—224no—
528C4×D4—224no—
529C4×D4—224no—
530C4×D4—224no—
531C4×D4—224no—
532C4×D4—248no—
533C4×D4—212no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—212no—
539C4×D4—212no—
540C4×D4—812no—
541C4×D4—812no—
542#117—212no—
543#117—24no—
544#117—224no—
545#117—224no—
546#117—224no—
547#117—224no—
548#117—212no—
549#117—212no—
550#117—224no—
551#117—46no—
552C2×C4⋊C4—212no—
553C2×C4⋊C4—212no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—224no—
556C2×C4⋊C4—224no—
557C2×C4⋊C4—248no—
558C2×C4⋊C4—212no—
559C2×C4⋊C4C2×D4124yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C24112yes—
589C2×C4⋊C4C24112yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2413yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C22⋊C4—212no—
596C2×C22⋊C4—212no—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2413yes—
602C2×C22⋊C4C2411yescharacteristic
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2411yescharacteristic
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2411yescharacteristic
612C2×C22⋊C4C2411yescharacteristic
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C24112yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2416yes—
632C2×C22⋊C4C2411yescharacteristic
633C2×C42—212no—
634C2×C42C2×D4124yes—
635C2×C42C2416yes—
636C2×C42C2416yes—
637C2×C42C2416yes—
638C2×C42C2413yes—
639C2×C42C2413yes—
640C2×C42C2412yes—
641C2×C42C2416yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2413yes—
647C2×C42C2413yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2416yes—
654#95C2412yes—
655#95C2412yes—
656#95C2412yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C24112yes—
662#95C2416yes—
663#95C24112yes—
664#95C2416yes—
665#95C24112yes—
666#95C2412yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671C24—26no—
672C24—212no—
673C24—26no—
674C24—26no—
675C24—46no—
676C24C2511yescharacteristic
677C24C2513yes—
678C24C2516yes—
679C24C2511yescharacteristic
680#41—2192no—
681#41—264no—
682#41—416no—
683C2×Q8—232no—
684C2×Q8—26no—
685C2×Q8—26no—
686C2×Q8—212no—
687C2×Q8—212no—
688C2×Q8—46no—
689C2×Q8—416no—
690C2×Q8C22×D4112yes—
691C2×Q8C22×D414yes—
692C2×Q8C2×#4118yes—
693C2×D4—296no—
694C2×D4—224no—
695C2×D4—26no—
696C2×D4—22no—
697C2×D4—212no—
698C2×D4—26no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—26no—
702C2×D4—212no—
703C2×D4—224no—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—26no—
707C2×D4—26no—
708C2×D4—212no—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—46no—
712C2×D4—412no—
713C2×D4—46no—
714C2×D4—412no—
715C2×D4—46no—
716C2×D4—46no—
717C2×D4C2×#41124yes—
718C22×C4—296no—
719C22×C4—22no—
720C22×C4—212no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—212no—
724C22×C4—212no—
725C22×C4—24no—
726C22×C4—212no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—22no—
730C22×C4—26no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—212no—
736C22×C4—212no—
737C22×C4—224no—
738C22×C4—224no—
739C22×C4—212no—
740C22×C4—46no—
741C22×C4—46no—
742C22×C4—412no—
743C22×C4—412no—
744C22×C4—412no—
745C22×C4—412no—
746C22×C4—412no—
747C22×C4—848no—
748C22×C4C22×D4112yes—
749C22×C4C22×D414yes—
750C22×C4C22×D4112yes—
751C22×C4C2×#41124yes—
752C22×C4C2512yes—
753C22×C4C2516yes—
754C22×C4C2516yes—
755C22×C4C2512yes—
756C22×C4C2513yes—
757C22×C4C2511yescharacteristic
758C22×C4C2513yes—
759C22×C4C2516yes—
760C22×C4C2511yescharacteristic
761C22×C4C2511yescharacteristic
762C22×C4C2513yes—
763C22×C4C2513yes—
764C22×C4C2513yes—
765C22×C4C2513yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2512yes—
769C22×C4C2512yes—
770C22×C4C2513yes—
771C4⋊C4—212no—
772C4⋊C4—212no—
773C4⋊C4—212no—
774C4⋊C4—212no—
775C4⋊C4—26no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—26no—
779C4⋊C4—22no—
780C4⋊C4—26no—
781C4⋊C4—26no—
782C4⋊C4—26no—
783C4⋊C4—26no—
784C4⋊C4—212no—
785C4⋊C4—26no—
786C4⋊C4—26no—
787C4⋊C4—212no—
788C4⋊C4—26no—
789C4⋊C4—22no—
790C4⋊C4—26no—
791C4⋊C4—24no—
792C4⋊C4—212no—
793C4⋊C4—212no—
794C4⋊C4—212no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—46no—
798C4⋊C4—46no—
799C4⋊C4—412no—
800C4⋊C4—412no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4C22×D4112yes—
804C4⋊C4C22×D4112yes—
805C4⋊C4C22×D4124yes—
806C22⋊C4—22no—
807C22⋊C4—26no—
808C22⋊C4—212no—
809C22⋊C4—212no—
810C22⋊C4—224no—
811C22⋊C4—22no—
812C22⋊C4—26no—
813C22⋊C4—26no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—212no—
818C22⋊C4—26no—
819C22⋊C4—22no—
820C22⋊C4—26no—
821C22⋊C4—26no—
822C22⋊C4—26no—
823C22⋊C4—212no—
824C22⋊C4—22no—
825C22⋊C4—212no—
826C22⋊C4—26no—
827C22⋊C4—26no—
828C22⋊C4—24no—
829C22⋊C4—212no—
830C22⋊C4—212no—
831C22⋊C4—24no—
832C22⋊C4—46no—
833C22⋊C4—46no—
834C22⋊C4—412no—
835C22⋊C4—412no—
836C22⋊C4—46no—
837C22⋊C4—412no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C42−1+414yes—
842C42—212no—
843C42—212no—
844C42—212no—
845C42—26no—
846C42—26no—
847C42—212no—
848C42—212no—
849C42—24no—
850C42—46no—
851C42—46no—
852C42—46no—
853C42C22×D4112yes—
854C42C22×D4112yes—
855C42C22×D4112yes—
856C42C22×D4112yes—
857C23—22no—
858C23—22no—
859C23—224no—
860C23—26no—
861C23—26no—
862C23—26no—
863C23—26no—
864C23—26no—
865C23—26no—
866C23—23no—
867C23—21no—
868C23—22no—
869C23—26no—
870C23—21no—
871C23—23no—
872C23—23no—
873C23—21no—
874C23—26no—
875C23—22no—
876C23—424no—
877C23—424no—
878C23—412no—
879C23—412no—
880C23C23×D412yes—
881C23C22×#41112yes—
882C23C2×2−1+412yes—
883C23#58512yes—
884C23C2611yescharacteristic
885Q8—224no—
886Q8—412no—
887Q8—86no—
888Q8#525116yes—
889D4—248no—
890D4—248no—
891D4—424no—
892D4—412no—
893D4—44no—
894D4—412no—
895D4—86no—
896D4—812no—
897D4—824no—
898C2×C4—28no—
899C2×C4—248no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—26no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—26no—
910C2×C4—26no—
911C2×C4—28no—
912C2×C4—224no—
913C2×C4—248no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—23no—
917C2×C4—21no—
918C2×C4—23no—
919C2×C4—26no—
920C2×C4—23no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—26no—
924C2×C4—26no—
925C2×C4—22no—
926C2×C4—26no—
927C2×C4—22no—
928C2×C4—23no—
929C2×C4—22no—
930C2×C4—21no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—21no—
934C2×C4—23no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—26no—
938C2×C4—26no—
939C2×C4—26no—
940C2×C4—22no—
941C2×C4—26no—
942C2×C4—26no—
943C2×C4—412no—
944C2×C4—412no—
945C2×C4—44no—
946C2×C4—412no—
947C2×C4—412no—
948C2×C4—812no—
949C2×C4—824no—
950C2×C4—824no—
951C2×C4C23×D416yes—
952C2×C4C23×D416yes—
953C2×C4C23×D412yes—
954C2×C4C23×D412yes—
955C2×C4C23×D416yes—
956C2×C4C23×D416yes—
957C2×C4C22×#4114yes—
958C2×C4C22×#41112yes—
959C2×C4C2×2−1+414yes—
960C22—24no—
961C22—24no—
962C22—22no—
963C22—22no—
964C22—212no—
965C22—212no—
966C22—212no—
967C22—448no—
968C22—46no—
969C22—46no—
970C22—46no—
971C22—46no—
972C22—46no—
973C22—42no—
974C22—42no—
975C22—46no—
976C22—41no—
977C22—43no—
978C22—43no—
979C22—41no—
980C22—41no—
981C22—43no—
982C22#349714yes—
983C22C24×D411yescharacteristic
984C22C23×#4112yes—
985C22C22×2−1+411yescharacteristic
986C22C2×#58511yescharacteristic
987C22H(7,𝔽2)12yes—
988C4—24no—
989C4—22no—
990C4—22no—
991C4—26no—
992C4—26no—
993C4—24no—
994C4—26no—
995C4—42no—
996C4—46no—
997C4—46no—
998C4—42no—
999C4—43no—
1000C4—41no—
1001C4—46no—
1002C4—43no—
1003C4—41no—
1004C4—41no—
1005C4—43no—
1006C4C2×#525112yes—
1007C2—24no—
1008C2—412no—
1009C2—83no—
1010C2—81no—
1011C2C22×#52511yescharacteristic
1012C2C2×#349711yescharacteristic
1013C2#6285211yescharacteristic
1014C2#6300012yes—
1015C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3516C2semidirect
2. C22×#520C2semidirect
3. #36581C2semidirect
4. #36578C2semidirect
5. #36546C2semidirect
6. Q8×#123C2semidirect
7. #36529C2semidirect
8. #36528C2semidirect
9. #36429C2semidirect
10. #36428C2semidirect
11. #35831C2semidirect
12. #35816C2semidirect
13. #35787C2semidirect
14. #35772C2semidirect
15. #35625C2semidirect
16. #35539C2semidirect
17. #35302C2semidirect
18. #35236C2semidirect
19. #34965C2semidirect
20. #34877C2semidirect
21. #34313C2semidirect
22. #34312C2semidirect
23. Q8×#117C2semidirect
26. C2×#557C22semidirect
27. C2×#556C22semidirect
30. C2×#552C22semidirect
35. C2×#548C22semidirect
36. C2×#542C22semidirect
37. C2×#541C22semidirect
45. C2×#520C22semidirect
46. C2×#519C22semidirect
59. #2636C22semidirect
60. #2636C22semidirect
61. #2629C22semidirect
62. #2620C22semidirect
63. #2611C22semidirect
64. #2610C22semidirect
65. #2609C22semidirect
66. #2603C22semidirect
67. #2601C22semidirect
68. #2601C22semidirect
69. #2601C22semidirect
73. #2566C22semidirect
74. #2562C22semidirect
76. #2544C22semidirect
77. #2540C22semidirect
79. #2538C22semidirect
80. #2537C22semidirect
86. #2481C22semidirect
87. #2473C22semidirect
88. #2467C22semidirect
89. #2463C22semidirect
90. #2460C22semidirect
91. #2456C22semidirect
92. #2454C22semidirect
93. #2452C22semidirect
94. #2449C22semidirect
95. #2448C22semidirect
96. #2446C22semidirect
97. #2443C22semidirect
98. #2442C22semidirect
99. #2440C22semidirect
104. #2428C22semidirect
105. #2427C22semidirect
106. #2423C22semidirect
107. #2421C22semidirect
108. #2417C22semidirect
109. #2416C22semidirect
119. #2396C22semidirect
120. #2392C22semidirect
121. #2392C22semidirect
122. #2367C22semidirect
123. #2366C22semidirect
124. #2363C22semidirect
125. #2361C22semidirect
126. #2361C22semidirect
127. #2360C22semidirect
128. #2355C22semidirect
129. #2352C22semidirect
130. #2351C22semidirect
131. Q8×C4⋊C4C22semidirect
132. Q8×C4⋊C4C22semidirect
133. D4×C4⋊C4C22semidirect
138. #2341C22semidirect
141. Q8×C22⋊C4C22semidirect
142. #2324C22semidirect
143. #2324C22semidirect
144. #2324C22semidirect
145. #2323C22semidirect
146. C4×#127C22semidirect
147. C4×#124C22semidirect
154. #2295C22semidirect
155. #2293C22semidirect
156. #2293C22semidirect
158. C42×Q8C22semidirect
229. C2×C4×Q8D4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35162
C22×#5202
#365812
#365782
#365462
Q8×#1232
#365292
#365282
#364292
#364282
#358312
#358162
#357872
#357722
#356252
#355392
#353022
#352362
#349652
#348772
#343132
#343122
Q8×#1172